I've lost count of all the times I've been told that feminism is dead. I've even found myself described as a "post-feminist" writer, as if I were one of the survivors of a lost golden age. I've never taken it very seriously, because I know that writing off political movements is a mug's game. But now feminism is back, and in such a big way that I can't help wondering how all those doomsayers are feeling.

A lively internet campaign to get rid of Page 3 has collected more than 100,000 signatures and received the support of the Girl Guides. Another campaign, The Women's Room, is encouraging women to add their names to a database of female experts to counter male bias in the media. And the pioneering feminist magazine Spare Rib is being relaunched in both paper and online editions.

I'm not in the least surprised. Feminism is one of the great human rights movements, and a raft of evidence shows that it is more necessary than ever. None of the big issues has gone away since I began writing Misogynies a quarter of a century ago; I seem to have been writing about equal pay throughout my career, and I'm still waiting for a government that will enforce the transparency we need to achieve it. Domestic violence accounts for one in seven recorded crimes of violence, while the exposure of "historic" rape cases on an industrial scale suggests that a culture of impunity existed for decades at such organisations as the BBC.

Two things combined to force feminism into the semi-underground it's now emerging from so triumphantly. Like any transformative movement, feminism threatened the status quo, unsettling powerful men in business, politics and the media who saw their interests threatened. The movement was actually very diverse, encompassing radical feminists and women who worked in traditional political movements, but we were all caricatured. The slander worked, turning off younger women who didn't want to be associated with the feminist label.

At the same time, feminist campaigns against the most egregious forms of sexism had begun to pay off, so younger women didn't encounter them in the way my generation had. When I asked to study economics A level in the 1970s, I was told it wasn't taught at my all-girls state school; when I started work on a local paper, the features editor assured me it wouldn't be long before I could stop covering court cases and write about fashion. Thanks to the efforts of 70s and 80s feminists, some of that reflexive sexism has gone into decline, or at least become less visible. For many women in their 20s or early 30s, it's only when discussions about pay, promotion and childcare kick in that they realise it's still a man's world in too many ways.

Journalism looks like a model of equal opportunities but three-quarters of news reporters on national titles are men, and women account for only a third of journalists covering politics and business. Rebekah Brooks, who was the most powerful female newspaper executive in the country until just before her arrest in the phone-hacking scandal, modelled herself on her most ambitious male colleagues — and cultivated exclusively male mentors.

For anyone who believes gender equality is no longer an issue, the economic crisis is a wakeup call. Unemployment among women rose by almost 20% between 2009 and 2012, compared with 0.32% among men. Vital services for women, including shelters for victims of domestic violence and trafficking, were among the first to feel the Coalition government's axe. I'm sure some of the feminist energy that is around at the moment has been generated by the urgent need to protect women's interests. But it's also a reaction to the growth of a vast commercial sex industry, which has flooded popular culture with crude sexual images of women.

The legal side of the industry is visible in billboards advertising pole dancing clubs, targeted at high-earners in the City. But there's also a huge illegal trade in the transport of girls and women across continents to provide sexual "services" to men in developed countries. Such things were unheard of when I wrote Misogynies and while I was aware of the horrors of female genital mutilation, I didn't know it was happening in the UK.

In the light of all this, it would be amazing if feminism wasn't undergoing a revival. One change for the better is the existence of the internet, which means campaigns can quickly become international. The SlutWalks movement started in Canada and was imported into the UK, where it updated the old Take Back the Night protests. I love seeing women asserting the right to be sexual on their own terms in a culture that promotes extreme images of women, from the preposterous "glamour" model Katie Price to the curiously sexless Duchess of Cambridge. And while I'm queasy about the nickname "blue bra girl", the brutal beating of a young woman in Cairo's Tahrir Square has become a symbol of the sexual harassment suffered by Arab women every day.

Women's rights are human rights. It's one of my favourite slogans. Twenty-first-century feminism is about girls' education, safe contraception and abortion, freedom from sexual and domestic violence, and the right to enjoy public space. It's a vibrant and radical manifesto for a supposedly defunct movement.

• The Public Woman by Joan Smith has just been published by the Westbourne Press